REMOTE SENS. ENVIRON. 44:231-238 (1993)

Estimating Snow Grain Size Using AVIRIS Data Anne W. Nolin and Jeff Dozier Department of Geography and Center for Remote Sensing and Environmental Optics, University of California, Santa Barbara

E s t i m a t e s of snow grain size for the near-surface snow layer were calculated for the Tioga Pass region and Mammoth Mountain in the Sierra Nevada, California, using an inversion technique and data collected by the Airborne Visible/Infrared Imaging Spectrometer (A VIRIS). The inversion method takes advantage of the sensitivity of near-infrared snowpack reflectance to snow grain size. The Tioga Pass and Mammoth Mountain single-band A VIRIS radiance images were atmospherically corrected to obtain surface reflectance. Given the solar and viewing geometry for the time and location of each A VIRIS overflight, a discrete-ordinate model was used to calculate directional reflectance as a function of snowpack grain size, for a wide range of snow grain radii. The resulting radius vs. reflectance curves were each fit using a nonlinear leastsquares technique which provided a means of transforming surface reflectance in each A VIRIS image to optically equivalent grain size on a per-pixel basis. This inversion technique has been validated using a combination of ground-based reflectance measurements and grain size measurements derived from stereologic analysis of snow samples for a wide range of snow grain sizes. The model results and grain size estimates derived from the A VIRIS data show that, for solar incidence angles between Address correspondence to Anne W. Nolin, Computer Systems Lab / CRSEO Girvetz 1140, University of California, Santa Barbara, CA 93016-4060. Received 11 February 1992; revised 31 October 1992. 0034-4257 / 93 / $6.00 ©Elsevier Science Publishing Co. Inc., 1993 655 Avenue of the Americas, New York, NY 10010

0 ° and 30 °, the technique provides good estimates of grain size. Otherwise, the local angle of solar incidence must be known more exactly. This work provides the first quantitative estimates for grain size using data acquired from an airborne remote sensing instrument and is an important step in improving our ability to retrieve snow physical properties independent of field measurements. INTRODUCTION Recent research in snow science has focused on the hydrologic, climatologic, and hydrochemical significance of seasonal snowpacks. While snow hydrologists have long been involved in determining the quantity of water held by the snowpack and the timing of melt, of newly found importance is the hydrochemical process of chemical elution from the snowpack and its effects on the aquatic ecology of alpine watersheds. Spatial and temporal changes in snow grain size can help us to characterize the thermal state of the snowpack, and to estimate the timing and spatial distribution of snowmelt. Because snow is a highly reflecting natural substance of substantial extent, it also plays a significant role in the Earth's radiation balance. Wiscombe and Warren (1980) noted that increased ice grain size is primarily responsible for lower values of spectrally integrated albedo. Accurate parameterization of the temporal and spatial

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changes in albedo of seasonally snow-covered areas is essential for realistic input to climate models. Dozier et al. (1987), using the model of Wiscombe and Warren (1980) and NOAA-6 AVHRR data, concluded that it was "potentially possible" to determine snow grain size from remote sensing data. However, their results were difficult to interpret because of the width and position of the NOAA-6 AVHRR near-infrared band, which limits its sensitivity to snow grain size. At wavelengths less than 1.0/~m, snowpack reflectance is affected by the presence of absorbing impurities as well as by grain size (Warren and Wiscombe, 1980); therefore, a spectral band should be chosen to avoid confounding interpretations. For airborneand satellite-based measurements, this band should be located in a spectral region where atmospheric scattering and absorption are negligible so that when the radiance values are atmospherically corrected to surface reflectance, errors in the characterization of the atmosphere, particularly the atmospheric water vapor, are minimized. Qualitative estimates of grain size were produced by Dozier and Marks (1987) using Landsat TM data to classify snow-covered regions into relatively finegrain new snow and older, coarser-grained snow, but no ground truth measurements were made at the times of the overpasses. In a set of laboratory experiments, Hyv~irinen and Lammasniemi (1987) measured the near-infrared reflectance of snow grains in three size classes and related changes in a reflectance ratio of bands centered at 1.03/tm and 1.26/~m to changes in average grain diameter. While these previous studies have clearly shown that remote sensing holds promise for mapping snow grain size, they also pointed to the need for appropriate instrumentation and development of inversion approaches to obtain quantitative snow grain size estimates. Here, we show how snowpack reflectance in a single, narrow near-infrared spectral band can be inverted to obtain optically equivalent snow grain size. We discuss the basis for and show the results of applying this inversion technique to data collected using both ground-based spectrometers and image data collected with the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) instrument (Vane et al., 1993). AVIRIS is an airborne imaging spectrometer with 224 spectral bands from 0.4 ~m to 2.45 gm with a nominal sampling interval and spectral

response function (full width at half maximum) of 10 nm. This instrument provides us with the appropriate band location and narrow bandwidth for sensitivity to snow grain size. The instrument flies on the NASA ER-2 aircraft at an altitude of about 20 km above mean sea level and has a ground instantaneous field-of-view of 20 m. The objectives of this research were to a) develop a physically based technique to retrieve snow grain size from reflectance data, b) validate the results over a wide range of grain sizes, c) apply the technique to airborne remote sensing data, and d) assess the limitations of the technique in remote sensing applications.

GRAIN SIZE INVERSION M O D E L

The spectral reflectance of snow varies strongly with wavelength (Warren, 1982; Dozier, 1989). In the visible part of the spectrum (0.4-0.7 ~m), ice is weakly absorbing and strongly forwardscattering, and snow has a high reflectance. In the longwave infrared region (3-14/,tin), ice is highly absorbing, and therefore, snow is dark. The basis of our inversion technique relies on the moderate absorptivity of ice in the near-infrared wavelengths (0.7-3.0 ~m), particularly in the 0.71.3/~m spectral region where snow reflectance is most sensitive to the snow grain size. Figure 1 illustrates the relationship between spectral reflectance and ice grain radius in the spectral region from 0.4/tm to 2.5/~m. While there is little spectral dependence on grain radius in the visible wavelengths, reflectance decreases strongly with increasing grain size in the near-infrared wavelengths. To relate the optical properties of snowpacks to physical properties such as grain size, we rely on radiative transfer models. Given the Mie scattering parameters for spherical ice grains radii ranging from 40/~m to 2500/tm as input, a discreteordinate method for radiative transfer (Stamnes et al., 1988) was used to calculate spectral directional reflectance as a function of the optically equivalent ice grain radius. The discrete-ordinate model is preferred over a two-stream radiative transfer model because the former is able to calculate the angular distribution of reflected radiation rather than simply the hemispherically integrated reflectance as is calculated by the latter. Dirmhirn

Estimating Snow Grain Size 233

Discrete-ordinate model results

v,£

~5

Figure 1. Spectral reflectance of snow from 0.4-2.5/am as a function of grain size. Note the steep decrease in reflectance with increasing grain size in the spectral region between 0.7 /am and 1.3 /am. Calculations were made using a discrete-ordinate radiative transfer model,

and Eaton (1975) showed that the measured reflectance of snow varies greatly, depending on both solar and viewing geometries. Optical parameters needed for the discrete-ordinate model include optical thickness, single-scattering albedo, and asymmetry parameter (or a description of the scattering phase function); these are calculated from the snowpack physical properties: depth, bulk density, and grain size. Diffuse irradiance, substrate reflectance, and solar and viewing geometries are also required as model inputs. For semiinfinite snowpacks, that is, where the substrate reflectance results in less than a 1% change in the snowpack reflectance (Dozier et al, 1989),

snowpack depth and density have a negligible effect on snowpack reflectance (Bohren and Beschta, 1979). This leaves grain size as the property that exerts the greatest control over nearinfrared reflectance. As with the two-stream model, model calculations are made more tractable by making the assumption of spherically shaped ice crystals. The equivalent sphere is the one having the same volume-to-surface ratio as the nonspherical snow grain (Dobbins and Jizmagian, 1966). Mugnai and Wiscombe (1980) have shown that, for randomly oriented moderately nonspherical scatterers, it is valid to use this spherical assumption. However,

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this assumption may not hold for new snow nor for oriented snow microstructure. The wavelength of 1.04 p m was chosen because it is in a spectral region where reflectance is particularly sensitive to grain radius size. There is an additional advantage in using a band centered at that wavelength. In that spectral region there is little atmospheric scattering or attenuation allowing atmospheric correction of the AVIRIS radiance data to be virtually insensitive to errors in estimating molecular scattering or atmospheric water vapor content. As described earlier, the relationship between modeled optically equivalent sphere radius and snowpack reflectance depends on both the solar and viewing geometries. For a nadir viewing instrument over a fiat surface, only a knowledge of the solar geometry is required to calculate the angular reflectance. However, as shown in Figure 2, if the solar illumination angle is greater than 30 ° , it is necessary,

Figure 2. Snow reflectance modeled as a function of equivalent grain size for solar incident beam angles. There is little difference between the curves for solar incidence angles between 0 ° and 30 °.

0.8-

~ = 1.04

~tm

0.6-

R

-

0.4

}0° _ 30° 45°

0.2

to know the angle of solar incidence before proceeding with the calculation. For each image, a model-generated curve of reflectance vs. grain size was fit with an exponential model of the form R = a e b where R is the calculated grain radius and a and b are coefficients using a method of least-squares fitting. This established a functional relationship between grain size and surface reflectance for each AVIRIS singleband image that could be inverted to transform snowpack reflectance at 1.04/.tin to an estimate of snow grain size. In satellite and high-altitude image data, to obtain surface reflectance in an image, we must correct for the effects of the atmosphere. Conversion of AVIRIS spectral radiance values to surface reflectance values was done using LOWTRAN-7 (Kneizys et al., 1988) and a two-stream model. Running LOWTRAN-7 with the parameters for a midlatitude winter atmosphere and with a visibility of 125 km, values of atmospheric transmittance (T), single-scattering albedo (~), and asymmetry parameter (g) were generated. Atmospheric spectral transmittance was converted to optical thickness [r = -log(T)], and these parameters, r, ~, and g, were used to drive a radiative transfer model to obtain direct and diffuse irradiance at the surface and upwelling irradiance (Dubayah, 1990). The appropriate reflectance-to-grain size transformation was then applied to the each atmospherically corrected AVIRIS image. One should note that these optically equivalent grain radii do not represent depth-averaged grain sizes for the entire snowpack. Rather, they are strongly weighted by the snowpack surface layer grain size, and the representative sampling depth is itself a function of grain size. Light in a snowpack penetrates to greater depth in coarse-grained snow and therefore interacts with snow grains at greater depth than if the pack is comprised of small snow grains. Table 1 shows the relationship between transmittance of solar radiation and snow grain size.

INVERSION M O D E L VAIJDATION

60°

0 0

I

[

250

I

I

1

L

500 750 grain radius, p.m

[

I

1000

Validation for the inversion technique was achieved by comparing model estimates of grain radii with those measured using stereological techniques (Perla, 1982; Dozier et al., 1987). To validate the technique over a wide range of snow

Estimating Snow Grain Size 235

Table 1. T h e Snowpack D e p t h with T r a n s m i t t e d Light (at it = 1.04 gin) R e d u c e d to 1/e ( ~ 3 7 % ) of t h e A m o u n t I n c i d e n t at t h e Snow Surface, Calculated as a F u n c t i o n of Grain Size Grain Radius (gm)

Depth (cm)

50 100 200 500 1000

5.2 7.4 11.0 17.5 25.0

grain sizes, we made in situ field reflectance measurements of fine-grained new snow, mediumgrained older snow, and coarse-grained spring snow. We then compared the stereologically measured grain radii to the optically equivalent grain radii obtained using the near-infrared reflectance data as input to the inversion model. In all cases, snow samples were collected concurrently with reflectance measurements. Spectral reflectance measurements of coarsegrained snow were made with the Portable Instantaneous Display and Analysis Spectrometer (PIDAS). These data were collected in the Tioga Pass area of the Sierra Nevada, 26 May 1989 (concurrent with an AVIRIS overflight). A second instrument, a modified Spectron Engineering SE-590 spec-

trometer, was used to measure spectral reflectance of fine-grained and medium-grained snow at Mammoth Mountain from 25 to 29 April 1989. The modified sensor was able to measure infrared reflectance in 63 bands from 1.075/~m to 2.5/lm. For estimating grain size, the 1.075/~m band was used. During this 5-day period, the snowpack surface layer changed from fine, newly fallen snow to a melt-freeze crust with larger grains. Table 2 shows the close agreement between the grain radii measured from stereological analysis and those estimated by the inversion technique. Agreement is particularly good for small grains. For the medium-sized grains, the model-derived estimates fall between grain sizes for the melt-freeze crust and those of the smaller grains underlying the crust. Snow grain radii calculated from the PIDAS reflectance measurements are also close to those obtained from stereology.

APPLICATION TO AVIRIS DATA

Having successfully validated the technique over a wide range of snow grain sizes, we proceeded to apply the technique to AVIRIS data. AVIRIS scenes of two locations and dates were selected

Table 2. Results of G r o u n d Reflectance M e a s u r e m e n t - D e r i v e d Grain Radius and t h e Optically Equivalent Grain Radius Calculated from Stereologic Analysis of C o n c u r r e n t l y Collected Snow Samples Spectron SE-590 Measured Reflectance at it = 1.075 I~m

Sphere Radius from Stereology (l~m)

Sphere Radius from Model (gm)

0.687 0.683 0.684 0.680 0.684 0.636 0.653 0.659 0.600 0.600 0.660 0.620

150.5 (0-5 cm snow depth) a

150 140 140 150 140 180 160 150 390 390 260 340

PIDAS Reflectance Measurements' at 2 = 1.04 I~m

Sphere Radius from Stereology (IJm)

Sphere Radius from Model (l~m)

0.359 0.328 0.337

711 (0-10 cm snow depth) 617 (0-10 cm snow depth) 705 (0-10 cm snow depth)

620 720 670

393 (0-2 snow depth cm) b

A slightly larger grain size was measured at the 5-15 cm snow depth layer (161/tm). J' Smaller grain sizes were measured for the 3-7 cm snow depth layer (161/~m) and the 7-10 cm snow depth layer (153 ~tm).

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for this purpose: Tioga Pass on 26 May 1989 and Mammoth Mountain on 22 March 1991. Snow samples were collected at the time of each overflight for stereological analysis to measure grain size. After removing atmospheric effects and applying the inversion model to transform surface reflectance of snow-covered pixels to optically equivalent grain size, each image was color-coded to more clearly show the spatial distribution of grain sizes. In the Tioga Pass image (north is to the upper right), the late Spring snow was coarse-grained and the snowcover was discontinuous. Tioga Lake appears in the three-band colorcomposite image (Fig. 3) as an oblong body of water that, at the time of the overflight, was partially covered with slushy ice. The Tioga Pass road is visible in the image, running along the west side of the lake. Snow-covered pixels are

displayed as white and rock/soil and senesced vegetation are red-brown. Ground truth measurements were made in the snow-covered area to the lower left of the lake, adjacent to the road. Figure 4 is the Tioga Pass grain size map showing areas devoid of snow cover masked to black; colors varying from yellow to green to dark blue to light blue represent grain sizes ranging from 1500 /~m to 500/tm. Averaging over a 140-pixel region of continuous snow cover where our snow samples were collected, we calculated the mean grain radius to be 751 /tm, closely agreeing with the values determined from the snow samples (see Table 2). Figure 5 is a three-band color-composite image showing Mammoth Mountain Ski Area. Brightest areas are snow-covered (ski runs can be seen

Figure 4. In this color-coded grain size image of the TiFigure 3. This is an AVIRIS three-band color composite image of the Tioga Pass area (4.0 km x 5.5 km), in the Sierra Nevada, California, collected on 26 May 1989. Tioga Lake, the oblong feature in the upper right portion of the image, is partially ice-covered. Snow-covered pixels appear as white areas and rock/ soil and senesced vegetation are red-brown. Ground truth measurements were made in the snow covered area in the lower left corner of the image, adjacent to the road.

oga Pass area, snow grain radii ranging from 1500 Bm to 1000/~m are shaded from yellow to green, those ranging from 1000/tm to 650 btm are shaded from dark- to medium-blue and those ranging from 650/.tm to 425/tm are shaded from medium blue to very light blue. Pixels that were determined to be nonsnow have been masked to black. In this late Spring image, the snowpack can be characterized as mostly coarse-grained and discontinuous.

Estimating Snow Grain Size 237

Figure 5. This is an AVIRIS three-band color composite image of Mammoth Mountain (6.8 km x 8 kin), in the Sierra Nevada, California, collected on 22 March 1991. The top of mountain can be seen as a dark ridge running diagonallv across the image. Ski runs are visible at the top of the image. Bright areas are snow-covered, darker pixels are shaded snow and the darkest pixels are coniferous vegetation or rock.

at the top of the image), and dark regions are either rock or vegetation; north is to the upper right, and solar illumination is from the bottom of the scene. At the time of the overflight, the snowpack was 2-3 m deep over much of the mountain, and there was a layer of newly fallen snow. Particles in this layer were more crystalline in appearance than those in deeper layers. For this case, we should expect that the use of an "equivalent sphere" would be less appropriate than for the r o u n d e d grains that are typical of older snow. Stereologic measurements of snow samples collected at the study plot indicated that the grains had a preferred orientation with grain axes longer in the horizontal than in the vertical plane. The average grain radius was calculated to be 103.8/~m for the layer from 0 cm to 10 era. From the AVIRIS image, averaging over a 42pixel region centered over our study plot on the mountain, we calculated the mean grain radius to be 139 /2m. Although this estimate is slightly higher than the stereological estimate of 103/2m, it is still surprisingly close, considering that the grains were neither spherically shaped nor randomly oriented. The color-coded grain size map of Mammoth Mountain in Figure 6 shows that the distribution

Figure 6. In this color-coded grain size image of Mammoth Mountain, snow grain radii ranging from 700/2m to 400/~m are shaded from yellow to green, those ranging from 400/2m to 200/2m are shaded from dark- to medium-blue, and those ranging from 200 ?2m to 50/xm are shaded from medium-blue to very light blue. Pixels that were determined to be nonsnow have been masked to black. The effects of topography on estimates of grain size can be seen in this image as slopes that are directly illuminated are mapped as having the smallest grain size and shaded areas have larger estimated snow grain sizes. of the estimated grain sizes depends on the angle of illumination. Black pixels are bare areas, yellow pixels represent both snow underlying coniferous vegetation and shaded snow, and colors ranging from green to dark blue to light blue represent grain radii from 500 /2m to 50 /2m. Areas that face the sun appear brighter and are mapped as smaller snow grains. With our technique, based on snow spectral reflectance in only one spectral band, one must know the local angle of illumination to accurately estimate grain size. The date and time of overflight must be known to calculate the solar geometry and the area to be mapped must either be level or have accurate digital elevation data available so that the angle of incidence can be calculated. Unfortunately, digital elevation data rarely are available for alpine areas.

CONCLUSIONS Our results show that we can successfully estimate snow grain size in the near-surface layer of the snowpack using reflectance at an ideally placed band at 1.04/2m. This m e t h o d is based on

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t h e o r y and allows us to m a k e estimates of snow surface layer grain size that are i n d e p e n d e n t of field m e a s u r e m e n t s . Comparisons of grain size r e t r i e v e d from g r o u n d - b a s e d reflectance data and grain size m e a s u r e d from stereologic analysis of snow samples show close a g r e e m e n t for relatively fine-grained snow, m e d i u m - g r a i n e d older snow, and coarse-grained spring snow. Maps of snow grain size p r o d u c e d from AVIRIS images of the Tioga Pass region and M a m m o t h Mountain showed that retrieved particle sizes w e r e within the exp e c t e d physical range for the types of snow present at each overflight time a n d s h o w e d good a g r e e m e n t with m e a s u r e d values from snow samples from our test sites. The approach is limited by the n e e d to k n o w the angle of solar incidence, so if the t e c h n i q u e is to be u s e d in alpine areas digital elevation models m u s t be available. If these conditions are met, an optically equivalent grain size can be r e t r i e v e d from reflectance data to be u s e d in snowpack e n e r g y balance models, for initialization and updating, as well as in climate models, for m o r e accurate p a r a m e t e r i z a t i o n of spatial and temporal variations in snow albedo. Robert Davis, of the U.S. Army Cold Regions Research and Engineering Laboratory, helped with data collection and stereological analysis oJ snow samples. The Mammoth Mountain Ski Area provided essential support services for our study plot on Mammoth Mountain. AVIRIS data were provided by the Jet Propulsion Laboratory, Pasadena, California. This work was supported by NASA Grant NAGW-1265.

Dozier, J. (1989), Spectral signature of alpine snow cover from the Landsat Thematic Mapper, Remote Sens. Environ. 28:9-22. Dozier, J., and Marks, D. (1987), Snow mapping and classification from Landsat Thematic Mapper data, Ann. Glaciol. 9:97-103. Dozier, J., Davis, R. E., and Perla, R. (1987), On the objective analysis of snow microstructure, in Avalanche Formation, Movement and Effects (H. Gubler, Ed.), IAHS Publ. No. 162, Int. Assoc. Hydrol. Sci., Wallingford, U.K., pp. 49-59. Dozier, J., Davis, R. E., and Nolin, A.W. (1989), Reflectance and transmittance of snow at high spectral resolution, Proc. IGARSS '89:662-664. Dubayah, R. (1990), The Topographic Variability of ClearSky Solar Radiation, Ph.D. Dissertation, 174 pp., Dept. of Geography, Univ. of California, Santa Barbara. Hyv~irinen, T., and Lammasniemi, J. (1987), Infrared measurement of free-water content and grain size of snow, Opt. Eng. 26:342-348. Kneizys, F. X., Shettle, E. P., Abreu, L. W., et al. (1988), User's Guide to LOWTRAN7, Rep. AFGL-TR-88-0177, Air Force Geophys. Lab., Bedford, MA. Mugnai, A., and Wiscombe, W. J. (1980), Scattering of radiation by moderately nonspherical particles, J. Atmos. Sci. 37:1291-1307. Perla, R. (1982), Preparation of section planes in snow specimens, J. Glaciol. 28:199-204. Stamnes, K., Tsay, S., Wiscombe, W., and Jayaweera, K. (1988), Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media, Appl. Opt. 27:2502-2509. Vane, G., Green, R. O., Chrien, T. G., Enmark, H. T., Hansen, E. G., and Porter, W. M. (1993), The airborne visible / infrared imaging spectrometer (AVIRIS), Renugte Sens. Environ. 44:127-143.

REFERENCES

Warren, S. G. (1982), Optical properties of snow, Rev. Geophys. Space Phys. 20:67-89.

Bohren, C. F., and Beschta, R. L. (1979), Snowpack albedo and snow density, Cold Regions Sci. Technol. 1:47-50.

Warren, S. G., and Wiscombe, W. J. (1980), A model for the spectral albedo of snow, II, Snow containing atmospheric aerosols. J. Atmos. Sci. 37:2734-2745.

Dirmhirn, I., and Eaton, F. D. (1975), Some characteristics of the albedo of snow, J. Appl. Meteorol. 14:375-379. Dobbins, R. A., and Jizmagian, G. S. (1966), Optical scattering cross sections for polydispersions of dielectric spheres, J. Opt. Soc. Am. 56:1345-1350.

Wiscombe, W. J., and Warren, S. G. (1980), A model for the spectral albedo of snow, I, Pure snow, J. Atmos. Sci. 37: 2712-2733.